part of the orbit of any planet in which at some time or other it may not be seen from the earth. Every point of the path of each planet can therefore be observed; and although without waiting for such observation its course might be determined, yet it is material here to attend to the fact, that the whole orbit may be submitted to direct observation. The different planets, also present peculiar features by which each may be distinguished. Thus they are observed to be spherical bodies of various magnitudes: the surfaces of some of them are marked by peculiar modes of light and shade, which although variable and shifting, still, in each case, possess some prevailing and permanent characters by which the identity of the object may be established, even were there no other means of determining it. The sun is the common centre of attraction, the physical bond by which this planetary family are united, and prevented from wandering independently through the abyss of space. Each planet thus revolving in a circle has the same tendency to fly from the centre that a stone has when whirled in a sling. Why then, it will be asked, do not the planets yield to this natural tendency? What enables them to resist it? To this question no satisfactory answer can be given; but the fact that the tendency is resisted, being certain, the existence of some physical principle in which the means of such resistance resides is proved. As the tendency to fly off is directed from the centre of the sun, the opposing physical influence must consequently be directed towards that centre. This central influence is what has been called gravitation. Although we are still ignorant of the nature or proximate cause of this force, and of its modus operandi, we have obtained a perfect knowledge of the laws by which it acts; and this is all that is necessary or material to enable us to follow out its consequences. By virtue of this force of gravitation then, the planetary masses receive a tendency to drop towards the sun, which tendency equilibrates with the opposite tendency to fly away, produced by their orbitual motion. On the exact equilibrium of these two opposite physical principles depends the stability of the system: if the centrifugal tendency proceeding from the orbitual motion were in excess, the planets would fall off from the central body, and depart for ever into the depths of space; if, on the other hand, the central influence, or gravitation towards the sun, existed in excess, these bodies would gradually approach that luminary, and finally coalesce with his mass.

Besides these bodies, the greater part of which have been long known, and the motions of most of which have been in some degree understood even from remote antiquity, there is a still more numerous class of objects, whose appearances in the system were of

such a nature as to defy the powers of philosophical enquiry, until these powers received that prodigious accession of force which was conferred upon them by the discoveries of Newton. Unlike planets, Comets do not present to us those individual characters above mentioned, by which their identity may be determined none of them have been satisfactorily ascertained to be spherical bodies, nor indeed to have any definite shape. It is certain that many of them possess no solid matter, but are masses consisting entirely of aeriform or vaporous substances; others are so surrounded with this vaporous matter, that it is impossible, by any means of observation which we possess, to discover whether this vapour enshrouds within it any solid mass. The same vapour which thus envelopes the body (if such there be within it) also conceals from us its features and individual character; even the limits of the vapour itself are subject to great change in each individual comet; within a few days they are sometimes observed to increase or diminish some hundred-fold. A comet appearing at distant intervals presents, therefore, no very obvious means of recognition. A like extent of surrounding vapour would evidently be a fallible test of identity; and not less inconclusive would it be to infer diversity from a different extent of nebulosity.

If a comet, like a planet, revolved round the sun in an orbit nearly circular, it might be seen in every part of its path, and its identity might thus be established independently of any peculiar characters in its appearance. But such is not the course which comets are observed to take. These bodies usually are observed to rush into our system suddenly and unexpectedly from some particular quarter of the universe. They first follow in a straight line, or nearly so, the course by which they entered, and this course is commonly directed to some point not far removed from the sun. As they approach that luminary, their path becomes curved, at first slightly, but afterwards more and more, the curve being concave towards the sun. Having arrived at a certain least distance from the centre of our system, they again begin to recede from the sun, and as their distance increases, their path becomes less and less curved; until at length they shoot off in a straight course, and make their exit from our system towards some quarter of the universe wholly different from that from which they came.

We have stated that none of the planets depart much above or below the plane of the earth's orbit; it is quite otherwise with comets, which follow no certain law in this respect; some of them sweep the system nearly in the plane in which the planets move; others rush through it in curves, oblique in various

degrees to this plane; whilst some move in planes perpendicular to it. The planets also move round the sun all in one directioc. Comets, on the other hand, rebel against this law, and more some in one direction and some in another.

So far then as observation informs us we are left to decide between two suppositions-1. That the comet has entered the system for the first time; and that having swept behind the sun. it has emerged in a different direction, never to return: 2. This it moves in a large orbit, of which the sun is not the centre, bar. on the contrary, is placed very near the path of the body itself: that the comet is visible only in that part of its orbit which is in the immediate neighbourhood of the sun, but is invisible throughout that larger part, which perhaps extends through depths of space far beyond our most remote planet. If the latter supposi tion be adopted, it would follow that the same comet. after emerging from our system, would, after the lapse of a certa time, return to it, and pursue the same path, or Dearly the same path, round the sun as before. If then we find, after the lapse 5 a certain time, a comet following the same path whilst viste is a former comet was observed to follow, we infer that they also followed the same path during that much longer period in which they were beyond the sphere of our observation: and consequently we infer, with a high degree of probability, that the comets which thus follow precisely the same track, must be the same comet. We say with probability, because there is a poss lity, although it be a bare possibility, that two different comets should move precisely in the same orbit.

Now, let us suppose that, during the appearance of a comet, its path from day to day, or perhaps from hour to hour, is so carefully observed, that we could delineate it with a corresponding degree of accuracy in any plan or model of the system. This path would, as we have seen, form a very small fragment of its entire orbit; but if the nature of that orbit were known, the principles of geometry would also enable us to complete the curve. Thus, if a small are of a large circle be traced upon paper, every one conversant with geometry will be able to complete the circle, even though he be not told with what centre the small are was described, or with what length of radius. It is the same with other curves. Newton has proved that every mass of matter which is moved through the system, under the attracting infa ence of the sun, must, by its motion, trace one or other of those curves called conic sections; and that the curve must be so placed, that the centre of the sun shall be in that point which is called its focus. Now, conic sections are of three kinds; the ellipse, which is a curve of oval form, such that a point moving

on it would retrace the same course every revolution. But the other two species (called the parabola and hyperbola), consist of two branches diverging from their point of connexion in two different directions, and proceeding in those directions without ever again reuniting. If a body (as it might do by the established law of gravitation) entered our system by one branch of such a curve, it would, after sweeping behind the sun, emerge by the other branch never to return. Thus it appears, that either of the two suppositions which we have just made, would be compatible with the law of gravitation; and it is possible that some comets might move in ellipses, returning continually over the same path at stated intervals, while others, moving in parabolas or hyperbolas, entering our system for the first and only time, would emerge from it in another direction, and quit it for ever. It will perhaps be asked, if the orbits must be conic sections, with the sun in the focus, how is it that the planetary orbits are considered as circles? The fact is, the planetary orbits are not strictly circular, though very nearly so; they are ellipses, which are so slightly oval, that, when exhibited in a drawing, they would not be perceived to be so, unless their length and breadth were accurately measured. The centre of the sun, also, is in their focus, and not in their centre; but owing to their slightly oval form, the distance of the focus from the centre is very inconsiderable compared with their whole magnitude.*

On the appearance of a comet then, the first question which presents itself to the astronomical enquirer is, whether the same comet has ever appeared before? and the only means which he possesses of answering this enquiry is, by ascertaining, from such observations as may be made during its appearance, the exact path it follows; and this being known, to discover, by the principles of geometry, the nature of its orbit. If the orbit be found to be an ellipse, then the return of the comet would be certain, and the time of the return would be known by the magnitude of the ellipse. If the path, on the other hand, should appear to be either a parabola or hyperbola, then it would be equally certain that the comet had never been before in our system, and would never return to it.

But a difficulty of a peculiar nature obstructs the solution of this question. It so happens that the only part of the course of a comet which can ever be visible, is a portion, throughout which the ellipse, the parabola, and hyperbola so closely resemble one

* Even if the orbit were circular, with the sun in the centre, it would not be incompatible with the law of gravitation.

another, that no observations can be obtained with sufficient accuracy to enable us to distinguish one from the other. In fact, the observed path of any comet, while visible, may indifferently belong to an ellipse, parabola, or hyperbola.

There is, nevertheless, a certain degree of definiteness in the observed course of the body, which, although insufficient to enable us to say what the nature of the entire orbit may be, is still sufficiently exact to enable us to recognise any other comet, which moves, while visible, nearly in the same course. If then, after the lapse of a certain time, a comet should be found following that course, there would be a strong presumption that it is the same comet returning again to our system, after having traversed the invisible part of its orbit. This probability would be strengthened, if, on the two occasions, the body should present a similar appearance; although this is not essential to the identity, since, as has been stated, the same comet is observed to undergo considerable changes, even during a single appearance.

The time between the appearances of comets following nearly the same path being noted, the interval-the identity of the bodies being assumed-must either consist of a single period, or of two or more complete periods. The epoch which is usually taken as the commencement of a new revolution being the instant of time at which the comet is at its least distance from the sun, the place of the comet at that moment is called its perihelion. The period of a comet may, therefore, be defined to be the interval of time between two successive arrivals at its perihelion.

Having succeeded in identifying the path of any two comets, we are then in a condition to predict with some degree of probability the time at which the next appearance may be expected. It is certain-providing that it be the same comet-that it will arrive at its perihelion after the same interval nearly also that it may arrive at half the interval, or a third of the interval, or any other fraction corresponding to the possible number of unobserved appearances which may have taken place in the interval between those appearances from which its return has been predicted. The times, therefore, at which the comet may be looked for with a probability of finding it, may without difficulty be predicted; and if it has been a conspicuous body in the heavens on the occasion of its former appearances, there is a probability that the whole interval between these appearances constituted but one period, and that no return of the comet had escaped observation.

Such are the circumstances which may have been conceived to have presented themselves when the idea first occurred of attempting to ascertain the identity of former comets, and to dis